Context

Mathematics is a fundamental science for understanding the world around us. It helps us understand patterns, predict behaviors, and solve complex problems in various disciplines. One of the topics that helps us achieve these goals is the study of maximums and minimums of functions, especially quadratic functions, also known as quadratic functions.

Quadratic functions are characterized by having a second-degree algebraic expression. Furthermore, when represented on a graph, they take the form of a parabola. This is important because the parabola has unique properties, such as a point where the maximum or minimum value of the function is reached, depending on whether the parabola is facing upwards or downwards.

The concepts of maximum and minimum are linked to the idea of finding extreme values that a variable can reach within a certain context. In a function, these values represent the maximum and minimum heights that the curve reaches, that is, the highest or lowest point on the function's graph.

The importance of this topic is reflected in its various practical applications. In a factory, for example, the concept of maximums and minimums can be used to determine the ideal number of products to be produced in order to maximize profit and minimize costs. In physics, these concepts can be used to calculate the maximum height that an object reaches when launched upwards or to determine the minimum speed necessary for a satellite to be launched into space.

To delve deeper into this topic, we can use the following resources:

• Khan Academy: Quadratic Functions - This link presents various topics on quadratic functions, including the identification of maximum and minimum values.
• Professor Ferretto: Video Lesson Quadratic Function - Maximums and Minimums - In this video, Professor Ferretto explains dynamically and in an easy-to-understand way how to find the maximum and minimum points in a quadratic function.
• Só Matemática: Quadratic Functions - This site provides a complete explanation of quadratic functions, their elements and properties, including maximum and minimum points.

Practical Activity

Activity Title: The Planet of Maximums and Minimums

Project Objective

The objective of this activity is to apply the concepts of maximums and minimums and quadratic functions in the creation of an educational and interactive game. Students will put theoretical concepts into practice in a game creation project, enhancing their understanding of the topic and stimulating collaboration and teamwork.

Detailed Project Description

In this activity, groups will be responsible for planning and creating a digital game called 'The Planet of Maximums and Minimums'. The game should be based on scenarios where the player needs to solve problems involving the identification and calculation of maximum and minimum points of quadratic functions to progress in the game.

For example, in one of the scenarios, the player may be on a planet where they need to calculate the maximum height a rocket reaches when launched, and this maximum height is represented by a quadratic function.

The game should have a minimum of 3 scenarios with progressive difficulties, each with a different challenge involving quadratic functions and the identification of their maximum and minimum points. The game should be tested and adjusted by the group until it functions smoothly and coherently.

Required Materials

• Computers with internet access
• Game creation software (Unity, Godot, Scratch)
• Online educational resources for research (Khan Academy, Professor Ferretto, Só Matemática)

Step-by-Step Guide for the Activity

1. Students will form groups of 3 to 5 people.
2. Each group should choose game creation software and learn how to use it.
3. The groups should research and study the concept of quadratic functions and maximums and minimums.
4. With the acquired knowledge, the groups should plan the game, defining the story, characters, challenges, and how mathematical concepts will be incorporated.
5. Each group will create the game according to the plan, using the chosen software.
6. After creating the game, the group should test it to ensure it is functioning correctly and make adjustments if necessary.
7. Finally, students should write a report on the project, explaining the game's creation and how the concepts of maximums and minimums were applied.

Project deliverables include the created game and a written report. The report should be divided into four parts: Introduction, where students will contextualize the theme 'Maximums and Minimums' and explain its relevance to reality and the project's objective; Development, where students will describe the game creation process, the methodology used, challenges encountered, how the concepts of maximums and minimums were applied in the game, and the results obtained; Conclusion, where students will summarize the learnings and experiences gained during the project and their conclusions; and Bibliography, listing all research sources used during the project.